Question 26750
Just so you know (and maybe you made this problem up) but your problem doesn't work. Even if the whole amount is invested at 5%, John would still end up making more than $1000. {{{23000*.05 = 1150}}} That said, let's try to solve it anyway...

Presuming there's no compounding of interest (and since you didn't mention any I'll presume there isn't) This can be solved by a system of equations. Let's call the amount invested at 8% "x" and the amount invested at 5% "y". You know that the amount the bank invested must add up to $23000, thus our first equation is:

{{{x + y = 23000}}}

The other equation involves the rates of investment, which when multiplied by the principle amount, gives the total value from each investment. In other words, the amount gained from investment x = x*.08 and from y = y*.05. The problem tells us that when we add these investments, they'll total $1000. To "write that in math" we would write:
{{{x*.08 + y * .05 = 1000}}}

Now that we have our two equations, we can solve this system by substitution or elimination. Using elimination we can rewrite the first equation for x as:
{{{x = 23000 - y}}}

Putting that in for the second equation (replacing x) gives:
{{{(23000-y)*.08 + y * .05 = 1000}}} Distribute to get:
{{{1840 - .08y + .05y = 1000}}} Rearrange to get:
{{{- .08y + .05y = -840}}} Combine y's and get:
{{{-.03y = -840}}} Divide both sides by -.03 and get:
{{{y = 28000}}}

Putting back into this eqation:
{{{x = 23000 - y}}} using y = 28000 gives:
{{{x = 23000 - 28000}}} Subtract and get:
{{{x = -5000}}}

Seeing this number should raise some flags, since they invested $28000 at 5% and somehow invested NEGATIVE $5000 at 8%. Your bank is ripping you off, and giving you an average rate of LESS than the 5% they promised. To be exact, they're investing your money at an average rate of:
{{{1000/23000 = 4.35%}}}

But this should give you help as to the methods used to solve it. Try it again where you earn $1390 after a year instead of $1000. You should get $8000 invested at 8% and $15000 at 5%.